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Cryopreservation of the biological sample usually requires rapid cooling in order to suppress the growth of intracellular ice and to reach the temperature below the vitrification temperature. The ultra-rapid cooling technique by using liquid nitrogen is favorable because it is safe, inexpensive, and harmless in most cases. This paper describes the transient heat transfer phenomena when the object is suddenly plunged into subcooled liquid nitrogen. The heat transfer coefficient in this rapid cooling process is very different from that of the steady state boiling where the quasi-static approximation is made. The cooling experiment used 0.2 mm thick copper disk. The temperature history was precisely measured during cooling process under various subcooled conditions (from 65 K to 77 K) of liquid nitrogen. The data is used not only for analyzing the cooling rate but also for estimating the instantaneous heat transfer coefficients. Much attention has been paid to the very initial cooling period when the vapor has not formed before the film boiling region. The transient heat transfer is large at the initial stage of cooling, but soon after the transient effect disappears. It is shown that the duration of transient heat transfer strongly depends on the degree of subcooling. The application of transient heat transfer coefficient to the subcooled liquid nitrogen cooling for the cryopreservation of bulk biological sample is also discussed